Method for predicting bending performance of Steel / CFRP hybrid square tube based on different loading positions

Abstract

The invention provides a Steel / CFRP hybrid square tube bending performance prediction method based on different loading positions, and the method comprises the following steps: 1, carrying out the experimental research of a Steel / CFRP hybrid square tube under bias loading through arranging a bias loading experiment, forming a final deformation comparison, and achieving the analysis of the comparison of the mechanical properties of the Steel / CFRP hybrid square tube under different loading positions; step 2, constructing a finite element model of the Steel / CFRP hybrid square tube under bias loading; 3, a theoretical prediction model of the Steel / CFRP hybrid square tube under bias loading is constructed, and the influence of the bias distance on theoretical prediction energy absorption is obtained; 4, analyzing a multi-parameter coupling effect under bias loading; 5, analyzing bending characteristic influence factors; comprising the influence of different laying layer angles, the influence of different CFRP wrapping lengths and the influence of different pressing head shapes.

Description

Technical Field

[0001] The invention relates to the technical field of research on bending properties of Steel / CFRP mixed square tubes, in particular to a method for predicting the bending properties of Steel / CFRP mixed square tubes based on different loading positions. Background Art

[0002] Urban underground transportation systems, especially subways, have become an effective means to solve urban traffic congestion. As the backbone of urban public transportation, the operational safety of subways is of vital importance. Due to the high speed and high passenger capacity of subways, once a collision occurs, it may cause significant casualties and property losses. The severity of this problem has attracted widespread attention from all walks of life, especially in the context of rapid technological progress and high safety requirements, subway safety has become more prominent. Subway collision accidents often occur in the end area of ​​the subway head car, and the end anti-collision structure is the most important structure for absorbing energy and transmitting impact loads during a subway collision. If the end anti-collision structure is damaged by foreign objects, it will threaten the lives of drivers and passengers.

[0003] As an advanced material with light weight, high specific strength and high specific stiffness, carbon fiber composite material (CFRP for short) can significantly reduce the dead weight of rail vehicles, help reduce vehicle carbon emissions and energy consumption, and conform to the concept of sustainable transportation. CFRP materials also have excellent durability and corrosion resistance, which can extend the service life of vehicles and reduce maintenance costs. In addition, the design flexibility and good formability of CFRP materials make it possible to manufacture structural parts of various complex shapes to meet the needs of different train models and body designs. Therefore, more and more rail transit vehicles use carbon fiber materials to improve train performance and reduce energy consumption. For example: the driver's cab structure of the British intercity train Intercity125 uses CFRP materials, which reduces the weight of steel structures by 30% to 35%; the French TGV double-decker coach body uses CFRP materials formed by vacuum curing bag process and a large number of honeycomb sandwich structures, which reduces the weight by 25% compared with aluminum bodies. The N700 series vehicles released by Japan are equipped with carbon fiber composite roofs, which have achieved good weight reduction effects. The TTX trains put into operation in South Korea use CFRP roof, side walls and end wall structures, which reduce the weight by 28% compared with stainless steel body. In addition, the next-generation subway vehicle "CETROVO" proposed by CRRC in 2018 has the largest proportion of CFRP materials and the overall weight is reduced by about 30%.

[0004] However, despite the excellent mechanical properties of CFRP, its economic cost is much higher than that of traditional metal materials such as aluminum alloy and steel, which limits its application scope to a certain extent. In addition, from the perspective of structural performance, CFRP may experience unstable deformations such as local buckling and brittle fracture failure when subjected to transient impact loads, resulting in a significant decrease in its crashworthiness. In order to consider economic costs and crashworthiness while pursuing structural lightweighting, a feasible method is to introduce low-cost, high-ductility, and stable deformation metal materials into lightweight, high-specific strength, and high-specific stiffness CFRP to guide the deformation and failure process of the material in a more effective way.

[0005] Most of the collision energy generated in a collision accident is often absorbed by the axial deformation and bending deformation of the thin-walled structure. At present, some good results have been achieved in the research on the crashworthiness of thin-walled structures under axial load conditions. In the past, the research on crashworthiness under bending load conditions mainly focused on three-point bending conditions or pure bending conditions. However, in actual engineering structures, thin-walled structures do not exist independently. Their two ends are usually connected to other structural components to form a complete energy absorption system. For example, the two ends of the end anti-collision structure of a subway vehicle are fixed by the sill beam and the chassis. When the anti-collision structure collides with a large external object, it can be regarded as a bending loading behavior under end constraint conditions. Since the three-point bending condition or pure bending condition ignores the axial force, this may cause the design scheme to deviate from reality or be difficult to apply in engineering. The bending loading behavior of thin-walled structures under end constraint conditions is much more complicated. When large plastic deformation occurs under this boundary condition, axial force, bending moment and shear force often participate together. However, there are few reports on the bending behavior of Steel / CFRP hybrid thin-walled structures under end constraint conditions and their application in subway end anti-collision structures.

[0006] The end structure of a subway vehicle usually plays an important protective role when a collision occurs. Enhancing the load-bearing and energy-absorbing capacity of the anti-collision structure at the end of the subway as much as possible, reducing the structural mass, and reducing the degree of deformation after crushing to increase the living space of the driver and passengers has important research value and engineering significance for improving the collision safety performance of subway vehicles, alleviating environmental pollution caused by emissions, and achieving lightweighting. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions, clarify the matching relationship of multiple parameters under offset loading conditions, and characterize the influence mechanism of the ply angle, CFRP wrapping length and indenter shape on the evolution of bending characteristics under offset loading.

[0008] To achieve the above object, the present invention adopts the following technical solution: A method for predicting the bending performance of a Steel / CFRP hybrid square tube based on different loading positions comprises the following steps:

[0009] Step 1: Conduct an experimental study on the Steel / CFRP hybrid square tube under offset loading by arranging an offset loading experiment to form a final deformation comparison and analyze the mechanical properties of the Steel / CFRP hybrid square tube under different loading positions;

[0010] Step 2: Construct a finite element model of the Steel / CFRP hybrid square tube under offset loading;

[0011] Step 3: Construct a theoretical prediction model for Steel / CFRP hybrid square tubes under offset loading to obtain the effect of offset distance on the theoretically predicted energy absorption;

[0012] Step 4: Analyze the multi-parameter coupling effect under bias loading;

[0013] Step 5: Analyze the factors affecting the bending characteristics; including the influence of different ply angles, the influence of different CFRP wrapping lengths, and the influence of different indenter shapes.

[0014] In a preferred embodiment, in step 1: the quasi-static bending test of the Steel / CFRP hybrid square tube under offset loading is carried out on an MTS-322 hydraulic servo control testing machine, and both ends of the specimen are locked and fixed by the upper and lower clamping devices of the U-support frame, and also include a rectangular clamp block. By adjusting the relative position relationship between the rectangular clamp block and the U-shaped clamp, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions are studied, and different loading position test scenarios are set by adjusting different effective spans.

[0015] In a preferred embodiment, in step 2: the geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimen in the experiment, the degrees of freedom on both sides are constrained, the loading speed of the pressure head is set to 1000 mm / s, the downward compression displacement is set to 22 mm, and the grid sizes of the specimen and the pressure head are set to 2 mm and 5 mm, respectively; the offset distance ΔD of the pressure head loading is set, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube; the effective span of the Steel / CFRP hybrid square tube is 300 mm, and the offset distances ΔD of the 1 / 3 span loading condition and the 1 / 4 span loading condition are set to 50 mm and 75 mm, respectively.

[0016] In a preferred embodiment, step 3 includes an analytical solution for the large deflection of the Steel / CFRP hybrid square tube under offset loading; under the offset loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored; it is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and deform globally in an integral manner; three hybrid plastic hinges are developed at the loading position and the end support of the Steel / CFRP hybrid square tube; the span of the hybrid square tube is L, the loading point is located at a distance of L1 from the left support end, and the offset distance between the loading point and the center line of the span of the hybrid square tube is ΔD; under the external concentrated load P b The maximum deflection W of the mixed square tube occurs under the action of b ;

[0017] The equilibrium equation of the moment is obtained, as shown in formula (1):

[0018]

[0019] Where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b =M bm ; Transform formula (1) to obtain the concentrated load P b The lateral displacement W of the loading point b The relationship expression between is shown in formula (2).

[0020]

[0021] Assume that the total extension of the left free body with length L1 is a L , its calculation expression is shown in formula (3)

[0022] a L =a L1 +a L2 (3)

[0023] where a L1 and a L2 are the axial extensions of the left free body end;

[0024]

[0025] Combining equation (3) and equation (4) can further simplify equation (5)

[0026]

[0027] According to the geometric relationship, the left rotation angle ψ LThe calculation expression of is shown in formula (6):

[0028]

[0029] Similarly, assume that the total extension of the right free body with length L2 is b R , its calculation expression is shown in formula (7)

[0030] b R =b R1 +b R2 (7)

[0031] where b R1 and b R2 are the axial extensions of the left free body end respectively; according to the geometric relationship, formula (8)

[0032]

[0033] Combining equation (7) and equation (8) to further simplify equation (9)

[0034]

[0035] According to the geometric relationship, the right rotation angle ψ R The calculation expression of is shown in formula (10):

[0036]

[0037] The ratio of axial elongation to curvature and bending deflection W in the left and right free bodies b The relational expression of is shown in formula (11):

[0038]

[0039] On the other hand, the relevant flow rule for the plastic yield criterion is expressed as follows:

[0040]

[0041]

[0042] Combining equations (11), (12) and (13), we can obtain the expression of the bending deflection of the Steel / CFRP hybrid square tube under offset loading:

[0043]

[0044] Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 are expressed by the relationship between the offset distance and the span:

[0045] L1=L / 2+ΔD (15)

[0046] L2=L / 2-ΔD (16)

[0047] Substituting equations (11), (15), and (16) into equation (1), the calculation expression of the analytical solution of the large deflection of the Steel / CFRP hybrid square tube under offset loading is obtained, as shown in equation (17);

[0048]

[0049] Among them, t m Indicates Steel thickness, t c Indicates the thickness of CFRP, P b1 , P b2 , P b3 , P b4 is the loading load under different bending deflection Wb, σ m represents the material yield stress of Steel square tube, σ c Indicates the stress of Steel square tube in tension and compression;

[0050] For each interval stage in formula (17), b -W b The curve is integrated and the energy is accumulated. Therefore, the plastic bending deformation energy E of the Steel / CFRP hybrid square tube under offset loading is obtained. b and deflection W b The relational expression of is shown in formula (18);

[0051]

[0052] In a preferred embodiment, in step 4: the correlation between the steel thickness, the CFRP thickness, the section width and the offset distance is analyzed to find the main effect of the correlation between the steel thickness, the CFRP thickness, the section width and the offset distance on the response; the linear effect of the normalized design parameters is calculated using a linear regression model, wherein the value range of the normalized design parameters is mapped to [0, 1]; the calculation expression of the linear effect value between each design parameter x and the output response f(x) is shown in formula (19):

[0053] f(x)=b0+b1x (19)

[0054] The slope b1 of the line in the linear regression model represents the influence of the design parameters on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameters have almost no effect on the output response; if the line tends to be vertical, it means that the design parameters have a greater impact on the output response; a line with a positive slope indicates that the design parameters are positively correlated with the output response, and a negative slope indicates that the design parameters are negatively correlated with the output response.

[0055] In a preferred embodiment, in step 5: parameter analysis is used to study the influence of the ply angle, CFRP coating length and indenter shape on the bending characteristics of the Steel / CFRP hybrid square tube under offset loading conditions; the default boundary conditions of the 1 / 3 span loading condition are used, and the following geometric parameters of the Steel / CFRP hybrid square tube are set to default values: the span is set to 300 mm, the section width is 28 mm, the Steel thickness is 1 mm, the CFRP thickness is 1 mm, the thickness of each CFRP layer is 0.1 mm, the stacking order of the ply angle is [0° / 90° / 45° / -45°], the indenter diameter is 25 mm, and the indenter offset distance is 50 mm; when one influencing factor changes, the other factors remain at the default values.

[0056] Compared with the prior art, the present invention has the following beneficial effects: The present invention takes Steel / CFRP hybrid square tube as the research object, and reveals the bending performance of Steel / CFRP hybrid square tube under different loading positions based on experimental methods. The finite element model and theoretical prediction model of Steel / CFRP hybrid square tube under offset loading are constructed and verified, and the influence of offset distance on the bending energy absorption mechanism is revealed based on the theoretical prediction model. The influence of simultaneous changes in multiple parameter domains under offset loading on the bending characteristics is discussed. In addition, the influence of the ply angle, CFRP wrapping length and the shape of the pressure head on the bending characteristics is also explored. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Different positions of the preferred embodiment of the present invention are biased loading, wherein (a) is 1 / 3 span loading; (b) is 1 / 4 span loading; (c) is a test sample;

[0058] Figure 2 The 1 / 3 span loading test results of the Steel / CFRP hybrid square tube of the preferred embodiment of the present invention, wherein (a) is the load and displacement history curve of the 1 / 3 span loading, and (b) is the deformation process of the 1 / 3 span loading;

[0059] Figure 3 The experimental results of 1 / 4 span loading of Steel / CFRP hybrid square tubes of the preferred embodiment of the present invention are shown in FIG. 1 , wherein (a) is the load and displacement history curve of 1 / 4 span loading, and (b) is the deformation process of 1 / 4 span loading;

[0060] Figure 4 The final deformation shape of the Steel / CFRP hybrid square tube at different loading positions in the preferred embodiment of the present invention;

[0061] Figure 5 Comparison of the final intrusion displacement measurement results of the Steel / CFRP hybrid square tube at different loading positions in the preferred embodiment of the present invention;

[0062] Figure 6 The mechanical properties of Steel / CFRP hybrid square tubes under different loading positions of the preferred embodiment of the present invention are compared, wherein (a) is a comparison of load-displacement curves under different loading conditions, and (b) is a comparison of energy-displacement curves under different loading conditions;

[0063] Figure 7 The comparison of the crash resistance of Steel / CFRP hybrid square tubes under different loading positions in the preferred embodiment of the present invention, where (a) is the configuration of pipes EA and S with different materials. inv Comparison, (b) is the PCF and SEA comparison of different material configuration pipe fittings, (c) is the D comparison of different material configuration pipe fittings lmax ,MCF comparison;

[0064] Figure 8 The finite element model of the Steel / CFRP hybrid square tube under offset loading of the preferred embodiment of the present invention;

[0065] Fig. 9 The final deformation modes of the experiment and simulation of the preferred embodiment of the present invention are compared, wherein (a) is a 1 / 3 span loading condition; (b) is a 1 / 4 span loading condition;

[0066] Fig.10 Comparison of experimental and simulation results of Steel / CFRP hybrid square tubes under different offset loading conditions of the preferred embodiment of the present invention;

[0067] Fig.11 The final intrusion displacement comparison between the simulation and experiment of the Steel / CFRP hybrid square tube under different offset loading conditions of the preferred embodiment of the present invention;

[0068] Fig.12 Schematic diagram of the overall bending deformation mode of the plastic neutral axis of the Steel / CFRP hybrid square tube under offset loading in a preferred embodiment of the present invention, wherein (a) is the transverse cross-sectional profile under offset loading, and (b) is the axial force and moment acting on the free body;

[0069] Fig.13The mechanical properties of the Steel / CFRP hybrid square tube under the 1 / 3 span loading condition of the preferred embodiment of the present invention are compared between the experimental results and the theoretical prediction, wherein (a) is the load-displacement curve of the experimental results and the theoretical prediction, and (b) is the energy-displacement curve of the experimental results and the theoretical prediction;

[0070] Fig.14 The mechanical properties of the Steel / CFRP hybrid square tube under the 1 / 4 span loading condition of the preferred embodiment of the present invention are compared between the experimental results and the theoretical prediction, wherein (a) is the load-displacement curve of the experimental results and the theoretical prediction, and (b) is the energy-displacement curve of the experimental results and the theoretical prediction;

[0071] Fig.15 Comparison between theoretical prediction and simulation results of Steel / CFRP hybrid pipe under offset loading in the preferred embodiment of the present invention;

[0072] Fig.16 The comparison between the theoretical prediction EA and simulation results of the Steel / CFRP hybrid square tube at different offset distances in the preferred embodiment of the present invention;

[0073] Fig.17 The deformation modes of the Steel / CFRP hybrid square tube under different offset distances of the preferred embodiment of the present invention, wherein (a) is the pressure head offset distance ΔD=25mm, (b) is the pressure head offset distance ΔD=100mm;

[0074] Fig.18 The main effect analysis of each design parameter on the response of the preferred embodiment of the present invention is shown in Figure 1, where (a) is the main effect analysis of each parameter on EA, and (b) is the main effect analysis of each parameter on S inv (c) is the main effect analysis of each parameter on SEA, (d) is the main effect analysis of each parameter on PCF, (e) is the main effect analysis of each parameter on MCF, and (f) is the main effect analysis of each parameter on D lmax Main effect analysis of ;

[0075] Fig.19 The variation law of each response under the multi-parameter coupling of the preferred embodiment of the present invention, where (a) is the relationship between EA and t m ,t c (b) is the relationship between EA, b, ΔD, and (c) is S inv With t m ,t c The relationship between (d) and S inv The relationship between (b) and ΔD, (e) is the relationship between SEA and t m ,t c (f) is the relationship between SEA and b, ΔD, and (g) is the relationship between PCF and t m ,tc (h) is the relationship between PCF and b, ΔD, (i) is the relationship between MCF and t m ,t c (j) is the relationship between MCF, b, and ΔD, and (k) is the relationship between D lmax The relationship between ΔD and b, (l) is D lmax With t m ,t c relationship;

[0076] Fig. 20 Comparison of load-displacement curves of Steel / CFRP hybrid square tubes with different ply angles in a preferred embodiment of the present invention;

[0077] Fig.21 The final intrusion displacement comparison of Steel / CFRP hybrid square tubes with different ply angles in the preferred embodiment of the present invention;

[0078] Fig. 22 The crashworthiness index comparison of Steel / CFRP hybrid square tubes with different ply angles in the preferred embodiment of the present invention, where (a) is the S at different ply angles. inv , EA comparison, (b) is the PCF, SEA comparison of different ply angles, (c) is the D of different ply angles lmax ,MCF comparison;

[0079] Fig.23 It is a schematic diagram of the arrangement of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths according to a preferred embodiment of the present invention;

[0080] Fig.24 The final deformation mode of the Steel / CFRP hybrid square tube with different CFRP wrapping lengths according to the preferred embodiment of the present invention;

[0081] Fig.25 Comparison of load-displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths according to a preferred embodiment of the present invention;

[0082] Fig.26 Comparison of final intrusion displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths according to a preferred embodiment of the present invention;

[0083] Fig. 27 The crashworthiness index comparison of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths according to the preferred embodiment of the present invention is shown in Figure 1, where (a) is the S of different CFRP wrapping lengths. inv , EA comparison, (b) PCF, SEA comparison of different CFRP wrapping lengths, (c) D comparison of different CFRP wrapping lengths lmax,MCF comparison;

[0084] Fig.28 Schematic cross-sectional views of different pressure heads according to preferred embodiments of the present invention, wherein (a) is conical, (b) is circular, (c) is trapezoidal, and (d) is square.

[0085] Fig.29 The final deformation modes of the Steel / CFRP hybrid square tube under different shapes of indenters offset loading in the preferred embodiment of the present invention, wherein (a) is a conical indenter offset loading, (b) is a circular indenter offset loading, (c) is a trapezoidal indenter offset loading, and (d) is a square indenter offset loading;

[0086] Fig.30 Comparison of load-displacement curves of Steel / CFRP hybrid square tubes under offset loading of different shapes of indenters according to a preferred embodiment of the present invention;

[0087] Fig.31 Comparison of the final intrusion displacement curves of the Steel / CFRP hybrid square tube under the biased loading of different shapes of indenters according to the preferred embodiment of the present invention;

[0088] Fig.32 Comparison of crashworthiness index of Steel / CFRP hybrid square tube under offset loading with different indenter shapes in the preferred embodiment of the present invention, where (a) is S with different indenter shapes inv , EA comparison, (b) PCF, SEA comparison with different indenter shapes, (c) D lmax , MCF comparison. DETAILED DESCRIPTION

[0089] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0090] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0091] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0092] This embodiment includes the following steps:

[0093] Step 1: Mechanical properties analysis of Steel / CFRP hybrid square tubes at different loading positions

[0094] Step 11: Bias Loading Experiment Arrangement

[0095] The quasi-static bending test of Steel / CFRP hybrid square tube under offset loading was carried out on an MTS-322 hydraulic servo control testing machine. The experimental device layout details of the offset loading condition are as follows: Figure 1 As shown. Figure 1 It can be seen that the two ends of the specimen are locked and fixed by the upper and lower clamping devices of the U-support frame. In addition, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions are studied by adjusting the relative position relationship between the rectangular clamp and the U-shaped clamp. Figure 1 (a) is a 1 / 3 span loading test scenario, the effective span is 300 mm, the diameter of the circular indenter is 25 mm, and the distance between the indenter loading point and the left side of the U support frame is 100 mm, which is 1 / 3 of the effective span. Figure 1 (b) is a 1 / 4 span loading test scenario, where the distance between the pressure head loading point and the left side of the U support frame is 75 mm, which is 1 / 4 of the effective span. Figure 1 (c) is the test specimen, and the length of both specimens is 380 mm. Based on the vacuum bag molding preparation process introduced in Chapter 3, the carbon fiber prepreg is attached and coupled to the inner surface of the Steel tube in an alternating layer manner of [0° / 90° / 45° / -45°].

[0096] In addition, the circular indenter moves vertically downward at a loading speed of 2 mm / min, and the maximum loading displacement of the indenter is set to 22 mm, that is, when the indenter reaches the maximum displacement, the downward loading stops. After the loading is completed, the indenter moves upward at a speed of 4 mm / min to unload the load. Table 1 records the detailed information of the Steel / CFRP hybrid square tube samples under the two offset loading positions.

[0097] Table 1 Summary of geometric parameters of Steel / CFRP hybrid square tube

[0098]

[0099]

[0100] Step 12: Experimental study of Steel / CFRP hybrid square tube under offset loading

[0101] The experimental results of 1 / 3 span loading and 1 / 4 span loading of Steel / CFRP hybrid square tube under end restraint boundary conditions are shown in Figure 2. Figure 2 and Figure 3 As shown. Figure 2(a) and Figure 3 From the load-displacement curve during the loading process (a), it can be seen that the load-displacement curves of the two offset loading conditions show a similar growth trend. In addition, similar to mid-span loading, the load-displacement curves under the two offset loading conditions can also be divided into three stages: elastic loading, plastic deformation and elastic recovery. In the elastic loading stage, the load and displacement almost show a monotonically increasing trend; as the load increases, it enters the initial plastic deformation stage. Due to the failure behavior of the internal CFRP tube, the bearing capacity under the two offset conditions decreases to a certain extent. With the further participation of the axial force, the load curve gradually rises; with the increase of unloading displacement, the elastic deformation energy of the Steel / CFRP hybrid square tube gradually begins to release until it returns to the final deformation state. From Figure 2 (b) and Figure 3 From the deformation process of (b), it can be seen that the Steel / CFRP hybrid square tube under 1 / 3 span and 1 / 4 span loading undergoes overall bending deformation accompanied by local indentation formation, which increases with the increase of the indenter displacement until it reaches the maximum value in the entire quasi-static bending loading. As the indenter begins to unload upward until it returns to its initial position, marking the end of the elastic recovery stage.

[0102] Step 13: Final deformation comparison

[0103] The final deformation shapes of the Steel / CFRP hybrid square tube under three different loading positions are shown in Figure 2. Figure 4 As shown. Figure 4It can be observed that the specimens under three different loading positions all experienced local buckling in the indenter loading area and the two side end constraint areas, and formed three fixed plastic hinges. It can also be seen that the specimens under the three loading positions all underwent overall bending deformation, and a certain degree of local deformation occurred in the indenter loading area. The indenter indentation area formed by the upper surface contour under 1 / 2 span loading was the smallest. The closer the loading position is to the constraint end, the greater the local deformation in the indenter loading area. In addition, a careful observation of the indenter loading area shows that the Steel / CFRP hybrid square tube loaded with 1 / 2 span produced a symmetrical plastic deformation mode, and the indentation of the indenter and the indentation of the end constraint area were almost symmetrical about the mid-span. However, the Steel / CFRP hybrid square tube under 1 / 3 span and 1 / 4 span loading showed an asymmetric plastic deformation mode in the indenter loading area. Under the two offset loading conditions, the indentation of the indenter loading area tilted to the right to a certain extent, and the area of ​​the plastic deformation area on the left was significantly larger than that on the right, which was mainly caused by the unevenly distributed axial force on the left and right sides of the pipe fitting. The indentation inclination of the Steel / CFRP hybrid square tube loading area under 1 / 4 span loading is more obvious than that of the specimen under 1 / 3 span loading. This is because the loading position of the indenter under 1 / 4 span loading is closer to the constraint end, thus generating a greater shear force, resulting in a more obvious asymmetry of the indentation. Figure 4 As can be seen from (a), the Steel / CFRP hybrid square tube under mid-span loading has almost no obvious plastic deformation on its two side restraint ends; Figure 4 (b) and Figure 4 (c) shows that the left clamping area of ​​the Steel / CFRP hybrid square tube near the loading end has obvious local depression, and the degree of depression of the specimen under 1 / 4 span loading is the most serious. However, there is almost no plastic deformation in the clamping area on the right side of the specimen, which is due to the uneven shear force generated at both ends of the specimen under offset loading.

[0104] After the indenter is completely unloaded, the final deformation at the midpoint of the cross section of the bottom surface of the specimen needs to be measured. The left clamping end is regarded as the measurement starting point, and the measurement is made one by one to the right, with the interval between each measurement point set to 30mm. In the indenter loading area with a length of 70mm, the distance between the measurement points is densified to 10mm. The test results of the final intrusion displacement of the Steel / CFRP hybrid square tube under three loading positions are summarized as follows: Figure 5 Due to the accuracy of the ruler and the measurement error, the final cumulative error is limited to ±1mm.

[0105] from Figure 5It can be observed that, compared with the symmetrical pattern of the maximum intrusion displacement under mid-span loading, the maximum intrusion displacement of the Steel / CFRP hybrid square tube under 1 / 3 span loading and 1 / 4 span loading did not appear at the center of the indenter, but appeared on the right side of the center of the indenter, and the above-mentioned final deformation results also revealed this feature. In addition, it can be seen that the bending deflection of the lower surface contour of the specimen under 1 / 2 span loading is the largest, while the bending deflection of the lower surface contour of the specimen under 1 / 4 span loading is the smallest. Compared with the loading at the mid-span position, the smaller the overall deformation of the Steel / CFRP hybrid square tube is when the loading position is closer to the constraint end, and the contribution of the overall and local deformation to the final deformation also changes.

[0106] Step 14: Performance comparison of Steel / CFRP hybrid square tubes at different loading positions

[0107] The load-displacement and energy-displacement curves of Steel / CFRP hybrid square tubes at three different loading positions are shown in Figure 2. Figure 6 As shown. Figure 6 From the load-displacement curve (a), it can be seen that the load curves at three different loading positions gradually increase with the increase of loading displacement. When just entering the plastic stage, the bearing capacity decreases to a certain extent. Subsequently, under the action of axial force, the bearing capacity increases to a certain extent. When the loading displacement reaches the set 22mm, the pressure head begins to unload upward. In addition, it can be seen that the bearing capacity of the Steel / CFRP hybrid square tube under 1 / 3 span loading and 1 / 4 span loading is greater than that under mid-span loading. In addition, from Figure 6 (b) The energy-displacement curve clearly shows that the energy absorption of the Steel / CFRP hybrid square tube is the largest under 1 / 4 span loading, while the energy absorption of the Steel / CFRP hybrid square tube is the smallest under mid-span loading. This is because the closer the loading position is to the constraint end, the higher the degree of participation of the axial force, so the bearing capacity increases accordingly, and the energy absorption also increases.

[0108] In order to quantitatively analyze the crashworthiness of Steel / CFRP hybrid square tubes under different loading conditions, the crashworthiness indicators in the load-displacement and final intrusion displacement curves are extracted and summarized in Table 2. As can be seen from Table 2, the EA of the Steel / CFRP hybrid square tubes under 1 / 3 span loading condition and 1 / 4 span loading condition are 233.22 J and 259.35 J, respectively. inv 21.24cm respectively 2 and 20.69cm 2 , PCF are 11.74 kN and 13.27 kN, SEA are 0.648 J / g and 0.719 J / g, D lmaxThey are 12.78 mm and 12.64 mm respectively, and the corresponding MCFs are 10.60 kN and 11.79 kN respectively.

[0109] Table 2 Crashworthiness index of Steel / CFRP hybrid square tube under different loading positions

[0110]

[0111] In order to observe the changes in rules more intuitively, Figure 7 The line graph compares the crashworthiness of Steel / CFRP hybrid square tubes at different loading positions. Figure 7 By comparing the crashworthiness of the steel / CFRP hybrid square tube under 1 / 3 span loading, it can be found that the crashworthiness of the steel / CFRP hybrid square tube under 1 / 2 span loading and 1 / 4 span loading is between that under 1 / 2 span loading and 1 / 4 span loading. The closer the loading position is to the constraint end, the larger the EA is, and the corresponding SEA is also larger, while D lmax and the corresponding S inv The EA of the Steel / CFRP hybrid square tube under 1 / 3 span loading condition and 1 / 4 span loading condition is 14.62% and 27.46% higher than that under 1 / 2 span loading condition, respectively. inv The PCF and SEA performances were reduced by 0.84% ​​and 3.41% respectively, the PCF performances were increased by 7.51% and 21.52% respectively, the SEA performances were increased by 13.88% and 26.36% respectively, and the D lmax A decrease of 1.54% and 2.62% respectively.

[0112] Step 2: Finite element modeling and verification of Steel / CFRP hybrid square tube under offset loading

[0113] Step 21: Finite element modeling of Steel / CFRP hybrid square tube under offset loading

[0114] The finite element model of Steel / CFRP hybrid square tube under offset loading is as follows: Figure 8 As shown. The geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimen in the experiment. The degrees of freedom on both sides are constrained, the loading speed of the pressure head is set to 1000mm / s, the downward compression displacement is set to 22mm, and the mesh sizes of the specimen and the pressure head are set to 2mm and 5mm, respectively. In addition, in order to simulate the offset loading condition, the offset distance ΔD of the pressure head loading is set, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube. The effective span of the Steel / CFRP hybrid square tube is 300mm, and the offset distances ΔD of the 1 / 3 span loading condition and the 1 / 4 span loading condition are set to 50mm and 75mm, respectively.

[0115] Step 22: Simulation and experimental verification

[0116] Fig. 9 The final deformation modes of the Steel / CFRP hybrid square tube under the 1 / 3 span loading condition and the 1 / 4 span loading condition were compared between the simulation and the experiment, which is an important criterion for verifying the correctness of the finite element model. Fig. 9 The finite element simulation results show that the local indentation in the indenter loading area of ​​the Steel / CFRP hybrid square tube and the local buckling near the constraint end can be observed. As expected, the finite element model and the experimental Steel / CFRP hybrid square tube both produce asymmetric plastic deformation modes in the indenter loading area, which indicates that the finite element model under offset loading established in this chapter can effectively predict the three plastic hinge modes of the Steel / CFRP hybrid square tube.

[0117] Comparison of the force-displacement curves and energy-displacement curves of the simulation and experiment under 1 / 3 span loading condition and 1 / 4 span loading condition. Fig.10 As shown. Fig.10 It can be found that, whether in experiments or finite element simulations, the force-displacement curves of the Steel / CFRP hybrid square tubes all experience three stages: elastic loading, plastic deformation, and elastic recovery. And the load-displacement curves in each stage are in good agreement. In addition, for the two offset loading conditions, it can be seen that the energy-displacement curves in the simulation are in good agreement with the experimental results.

[0118] Comparison of final intrusion displacements of Steel / CFRP hybrid square tubes under different offset loading conditions between simulation and experiment Fig.11 As shown. Fig.11 It can be seen that the final intrusion displacement of the simulation and experimental measurement maintains a high degree of agreement, indicating that the measurement results of the lower surface deformation of the finite element model are reliable. The various crashworthiness indicators of the Steel / CFRP hybrid square tube simulation and experiment under the two loading conditions are listed in Table 3. It can be seen from Table 3 that EA, PCF and S under 1 / 3 span loading are inv The error values ​​of EA, PCF and S under 1 / 4 span loading are 4.17%, 1.70% and 1.51% respectively. inv The error values ​​are 2.84%, 2.94% and 1.40% respectively. The maximum errors of the crashworthiness indexes under the two offset conditions are less than 5%, indicating that the finite element model under offset loading established in this chapter can accurately predict the bending response and mechanical behavior of Steel / CFRP hybrid square tubes under end constraint boundary conditions.

[0119] Table 3 Comparison of crashworthiness indexes of Steel / CFRP hybrid square tubes under different offset loading conditions between simulation and experiment

[0120]

[0121] Step 3: Theoretical prediction model of Steel / CFRP hybrid structure under offset loading

[0122] Step 31: Analytical solution of large deflection of Steel / CFRP hybrid square tube under offset loading

[0123] Under the offset loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored. It is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and deform globally in an integral manner. Therefore, the simplified schematic diagram of the large deflection response of the neutral axis of the Steel / CFRP hybrid square tube under lateral offset loading is as follows: Fig.12 As shown. Fig.12 It can be seen that the Steel / CFRP hybrid square tube develops three hybrid plastic hinges at the loading position and the end support. The span of the hybrid square tube is L, and the loading point is located at L1 from the left support end. It can be regarded as the offset distance between the loading point and the center line of the span of the hybrid square tube is ΔD. b The mixed square tube has the maximum deflection W under the action of b .

[0124] according to Fig.12 The axial force and moment distributed on the free body in (b) can obtain the equilibrium equation of the moment, as shown in equation (1).

[0125]

[0126] Where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b =M bm Therefore, transform equation (1) to obtain the concentrated load P b The lateral displacement W of the loading point b The relationship expression between them is shown in formula (2).

[0127]

[0128] Assume that the total extension of the left free body with length L1 is a L , and its calculation expression is shown in formula (3).

[0129] a L =a L1 +a L2 (3)

[0130] where a L1 and a L2are the axial extensions of the left free body end. Fig.12 The geometric relationship in can be obtained as formula (4).

[0131]

[0132] Combining equation (3) and equation (4) can further simplify to obtain equation (5).

[0133]

[0134] According to the geometric relationship, the left rotation angle ψ L The calculation expression of is shown in formula (6).

[0135]

[0136] Similarly, assume that the total extension of the right free body with length L2 is b R , and its calculation expression is shown in formula (7).

[0137] b R =b R1 +b R2 (7)

[0138] where b R1 and b R2 are the axial extensions of the left free body end. According to the geometric relationship, we can get formula (8).

[0139]

[0140] Combining equation (7) and equation (8) can be further simplified to obtain equation (9).

[0141]

[0142] According to the geometric relationship, the right rotation angle ψ R The calculation expression of is shown in formula (10).

[0143]

[0144] The ratio of axial elongation to curvature and bending deflection W in the left and right free bodies b The relational expression of is shown in formula (11).

[0145]

[0146] On the other hand, the relevant flow rule for the plastic yield criterion can be expressed as follows:

[0147]

[0148] By combining equations (11), (12) and (13), we can get the expression for the bending deflection of Steel / CFRP hybrid square tube under offset loading.

[0149]

[0150] Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 can be expressed by the relationship between the offset distance and the span:

[0151] L1=L / 2+ΔD (15)

[0152] L2=L / 2-ΔD (16)

[0153] Substituting equations (11), (15), and (16) into equation (1), the calculation expression of the analytical solution for the large deflection of the Steel / CFRP hybrid square tube under offset loading is obtained, as shown in equation (17).

[0154]

[0155] For each interval stage in formula (17), b -W b The curve is integrated and the energy is accumulated, P b1 , P b2 , P b3 , P b4 is the loading load under different bending deflection Wb, σ m represents the material yield stress of Steel square tube, σ c represents the stress of the Steel square tube in tension and compression; therefore, the plastic bending deformation energy E of the Steel / CFRP hybrid square tube under offset loading can be obtained: b and deflection W b The relational expression of is shown in formula (18).

[0156]

[0157] Step 32: Verification of theoretical prediction model of Steel / CFRP hybrid structure under offset loading

[0158] In the experiment, the span of the Steel / CFRP hybrid square tube is L=300mm, and the thickness of the outer CFRP layer is t c =1mm, inner layer steel thickness t m =1mm, section width b = 28mm, σ m =240MPa,σ c=70MPa. In addition, the pressure head offset distance ΔD of the 1 / 3 span loading condition is 50mm, and the pressure head offset distance ΔD of the 1 / 4 span loading condition is 75mm. In order to verify the validity of the theoretical prediction model of the Steel / CFRP hybrid square tube under offset loading, the relevant geometric parameters are substituted into the analytical solution of the large deflection of the hybrid square tube in equations (17) and (18), and the mechanical properties comparison diagram between the experimental results and the theoretical prediction of the Steel / CFRP hybrid square tube under 1 / 3 span and 1 / 4 span loading conditions can be obtained, as shown in Figure 2. Fig.13 and Fig.14 shown.

[0159] from Fig.13 (a) and Fig.14 As can be seen from (a), for Steel / CFRP hybrid square tubes under different offset loading conditions, except for the initial elastic loading stage, the theoretical model cannot accurately predict the bending response of the Steel / CFRP hybrid square tube. The overall trend of the force-displacement curve calculated by the theoretical model in other stages is consistent with the experimental results. Fig.13 (b) and Fig.14 (b) shows that the energy-displacement curves predicted by the theoretical model for the two offset loading conditions are in good agreement with the experimental results. The energy absorption of the Steel / CFRP hybrid square tube under different loading conditions is summarized in Table 4. From the perspective of energy absorption, the maximum errors between the theoretical model prediction and the experimental results for the 1 / 3 span and 1 / 4 span loading conditions are 0.04% and 6.54%, respectively. This error is within the controllable range, indicating that the theoretical model of the Steel / CFRP hybrid square tube under offset loading can effectively predict the experimental results.

[0160] Table 4 Comparison of energy absorption between theoretical prediction and experimental results of Steel / CFRP hybrid tube under different loading conditions

[0161]

[0162] In order to further verify the accuracy of the theoretical model under offset loading, the theoretical model prediction results of Steel / CFRP hybrid square tubes with different spans, section widths, thicknesses and offset distances were compared with the simulation results. In addition, for the convenience of description, Steel / CFRP hybrid square tubes with different geometric dimensions and pressure head offset distances are named according to the specific meanings represented by the geometric parameters. For example: if the span of the Steel / CFRP hybrid square tube is L = 300mm, the section width b = 28mm, the thickness t = 2mm, and the pressure head offset distance ΔD = 25mm, the pipe fitting is named St / CF-L300b28t2ΔD25. It should be noted that for Steel / CFRP hybrid square tubes with different geometric parameters, the thickness of the outer layer Steel and the thickness of the inner layer CFRP are configured in a 1:1 ratio.

[0163] Comparison of the force-displacement curves predicted by the theoretical model of the Steel / CFRP hybrid tube with the simulation results, such as Fig.15 As shown. Fig.15 It can be seen that the theoretically predicted force-displacement curve is in good agreement with the simulation results. The comparison of the energy absorption of the theoretical model and finite element simulation of Steel / CFRP hybrid square tubes with different geometric parameters is shown in Table 5. As can be seen from Table 5, the maximum error between the theoretical results and the simulation results of the bending energy absorption of the Steel / CFRP square tube under offset loading is 6.16%, which is less than 10%, indicating that the error is within a controllable range. In addition, considering the agreement of the force-displacement curve and the accuracy of the bending energy absorption calculation, the theoretical model can accurately predict the force-displacement curve change trend and bending energy absorption of Steel / CFRP hybrid square tubes with different geometric parameters during offset loading in most cases.

[0164] Table 5 Comparison of energy absorption of Steel / CFRP hybrid square tubes with different geometric parameters

[0165]

[0166] Step 33: Effect of offset distance on theoretically predicted energy absorption

[0167] The influence of different offset distances ΔD on the energy absorption performance of Steel / CFRP hybrid square tubes under offset loading was further explored. To this end, the following geometric parameters of the Steel / CFRP hybrid square tube were set to default values: span of 300 mm, pressure head diameter of 25 mm, section width of 28 mm, CFRP thickness of 1 mm, thickness of each CFRP layer of 0.1 mm, and thickness of Steel of 1 mm.

[0168] The theoretical prediction EA and simulation results under different offset distances ΔD are compared, as shown in Fig.16 As shown. Fig.16It can be seen that the theoretically predicted EA value increases with the increase of the offset distance ΔD. However, when the offset distance ΔD is greater than 80mm, the gap between the simulated EA value and the theoretically predicted value gradually increases. This is mainly due to the excessive shear force on the end of the Steel / CFRP hybrid square tube. As the offset distance increases, the shear force also gradually increases. When the shear force is too large to be ignored, the dent will not only appear in the loading area under the pressure head, but also extend to other areas of the hybrid square tube, such as Fig.17 As shown. Fig.17 As can be seen from (a), the Steel / CFRP hybrid square tube with an offset distance of 25 mm almost presents an overall bending deformation mode; Fig.17 As can be seen from (b), the Steel / CFRP hybrid square tube has serious local depression near the left constraint end, which significantly reduces the EA of the tube under offset loading.

[0169] In summary, when the offset distance is less than 80 mm, the EA will increase with the increase of the offset distance, as predicted by the theory. However, if the offset distance is too large, the participation of shear force will significantly reduce the EA of the Steel / CFRP hybrid square tube.

[0170] Step 4: Analysis of multi-parameter coupling effects under bias loading

[0171] Step 41: Main Effects Analysis

[0172] Keeping the span constant, explore the changes in the bending behavior response of the Steel / CFRP hybrid square tube under the combination of multiple parameters when the Steel thickness, CFRP thickness, section width and offset distance change simultaneously, and study the influence of the simultaneous change of multiple parameter domains on the bending characteristics under offset loading. In order to scientifically statistically and effectively analyze the influence of each design parameter, this study selected four design parameters and gave them a certain range of variation according to actual conditions. The initial value and range of variation of each design parameter are shown in Table 6. In this study, a full factorial experimental design was used for sampling for the above four design parameters, and each design parameter took five parameter levels.

[0173] Table 6 Variation range of design parameters of Steel / CFRP hybrid square tube under offset loading

[0174]

[0175]

[0176] In the interpretation of the relationship between the bending characteristics of Steel / CFRP hybrid square tubes and multiple parameters under offset loading, an important analytical method is to determine the correlation between the parameters and find the main effect of each design parameter on the response. The main effect is the influence of a single design parameter on the response, which can be expressed in the form of a linear effect. In this study, a linear regression model is used to calculate the linear effect of the normalized design parameters, where the value range of the normalized design parameters is mapped to [0,1]. The calculation expression of the linear effect value between each design parameter x and the output response f(x) is shown in Equation (19).

[0177] f(x)=b0+b1x (19)

[0178] The slope b1 of the line in the linear regression model represents the degree of influence of the design parameters on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameters have almost no effect on the output response; if the line tends to be vertical, it means that the design parameters have a greater impact on the output response. A positive slope of the line indicates that the design parameters are positively correlated with the output response, and a negative slope indicates that the design parameters are negatively correlated with the output response. The main effect analysis of each design parameter on the response is shown in the figure below. Fig.18 As shown. Fig.18 The main effects plot shows that:

[0179] (1) Steel thickness t m The most significant impact on the response EA, PCF, and MCF is as follows: Steel thickness t m >Offset distance ΔD>CFRP thickness t c > Section width b. Steel thickness t m , offset distance ΔD, CFRP thickness t c , the section width b is positively correlated with EA, PCF and MCF.

[0180] (2) The effect of each design variable on the response S inv and D lmax The influence of is more complex, and the order of influence from large to small is: Steel thickness t m > Section width b > Offset distance ΔD > CFRP thickness t c . Where S inv , D lmax With Steel thickness t m are positively correlated with the cross-sectional width b, offset distance ΔD, and CFRP thickness t c Both are negatively correlated.

[0181] (3) The offset distance ΔD has the most significant effect on SEA, and the section width b has the least effect on SEA. The order of influence from large to small is: offset distance ΔD>CFRP thickness t c >Steel thickness t m > Section width b. Where SEA and Steel thickness t m is negatively correlated with the offset distance ΔD and CFRP thickness t c , and cross-sectional width b are positively correlated.

[0182] Step 42: Multi-parameter coupling effect analysis

[0183] Fig.19 The variation law of each response under the multi-parameter coupling is plotted. It can be seen intuitively that with the increase of Steel thickness t m The gradual increase of EA, PCF, MCF, S inv , D lmax Both showed a monotonically increasing trend, while SEA showed a monotonically decreasing trend. m It can increase energy absorption and load-bearing capacity, but it also increases the intrusion volume and intrusion area, which also produces a negative effect compared to energy absorption. c The increase in the CFRP thickness t c It is beneficial to reduce the intrusion amount and intrusion area and improve the specific energy absorption. Therefore, choosing the appropriate Steel and CFRP thickness is beneficial to improve the bending performance of the hybrid square tube. With the increase of the offset distance ΔD, EA, PCF, and MCF all show a monotonically increasing trend, and SEA shows a monotonically decreasing trend. With the increase of the cross-sectional width b, EA, PCF, and MCF all show a monotonically increasing trend, and S inv and D lmax It shows a monotonically decreasing trend and has little impact on SEA.

[0184] In summary, it can be found from the multi-parameter coupling effect that EA, PCF, MCF, S inv , D lmax The biggest influence is the steel thickness t m The offset distance ΔD has the greatest impact on SEA. This is because the closer the loading position is to the constraint end, the higher the degree of participation of the axial force, which leads to a greater load-bearing capacity and energy absorption, resulting in a larger SEA without changing the mass.

[0185] Step 5: Analysis of factors affecting step bending characteristics

[0186] Parametric analysis is used to study the effects of ply angle, CFRP coating length and indenter shape on the bending properties of Steel / CFRP hybrid square tubes under offset loading conditions. In this section, the default boundary conditions of the 1 / 3 span loading condition are used, and the following geometric parameters of the Steel / CFRP hybrid square tube are set to the default values: the span is set to 300 mm, the section width is 28 mm, the Steel thickness is 1 mm, the CFRP thickness is 1 mm, the thickness of each CFRP layer is 0.1 mm, the stacking order of the ply angle is [0° / 90° / 45° / -45°], the indenter diameter is 25 mm, and the indenter offset distance is 50 mm. When one influencing factor changes, the other factors remain at the default values.

[0187] Step 51: Effect of different ply angles

[0188] Under the end constraint boundary condition, the bending characteristics of the Steel / CFRP hybrid square tube are directly related to the ply angle. In order to gain a deeper understanding of the bending crushing mechanism, a parametric analysis of the Steel / CFRP hybrid square tube with different ply angles under 1 / 3 span loading condition was carried out.

[0189] Fig. 20 The load-displacement curves of Steel / CFRP hybrid square tubes with four different ply angles are compared when other parameters remain unchanged. Fig. 20 It can be seen that the load-displacement curve of the Steel / CFRP hybrid square tube with the ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] will significantly decrease in bearing capacity after entering the plastic deformation stage from the elastic loading stage. The load-displacement curve of the Steel / CFRP hybrid square tube with the ply angle of [45° / -45°] is relatively stable. This is because the CFRP tube with a 90° fiber ply will experience fiber breakage, which will lead to a decrease in load. The CFRP tube with a 45° fiber ply is mainly subjected to shear force during bending loading, so its load curve is relatively stable.

[0190] In addition, the final intrusion displacement of each measuring point is plotted on Fig.21 In. From Fig.21 It can be seen that the Steel / CFRP hybrid square tube with a layup angle of [0° / 90°] produces the largest intrusion, while the Steel / CFRP hybrid square tube with a layup angle of [45° / -45°] produces the smallest intrusion.

[0191] In addition, the crashworthiness indices extracted from the load-displacement and final intrusion displacement curves are summarized in Table 7. In order to observe the regular changes more intuitively, Fig. 22The histogram compares the crashworthiness of Steel / CFRP hybrid square tubes with different ply angles. Fig. 22 As can be seen from (a), the EA and S of the hybrid square tube with 90° fiber layup are inv The EA and S of the hybrid square tube with 45° fiber layup are relatively large. inv It can be seen from Table 7 that the EA of Steel / CFRP hybrid square tubes with ply angles of [0° / 90° / 45° / -45°], [0° / 90°] and [45° / -45°] are 223.49 J, 218.47 J and 203.25 J, respectively. inv 20.92cm respectively 2 、21.82cm 2 and 17.63cm 2 The EA of the Steel / CFRP hybrid square tube with the ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] is 9.96% and 7.49% higher than that of the Steel / CFRP hybrid square tube with the ply angle of [45° / -45°], respectively. inv An increase of 18.66% and 23.77% respectively.

[0192] from Fig. 22 From (b), it can be seen that the Steel / CFRP hybrid square tube with a ply angle of [0° / 90° / 45° / -45°] produces the highest SEA, the Steel / CFRP hybrid square tube with a ply angle of [0° / 90°] produces the highest PCF, and the hybrid square tube with a ply angle of [45° / -45°] has the lowest SEA and PCF. Fig. 22 (c) shows that the Steel / CFRP hybrid square tube with a ply angle of [0° / 90° / 45° / -45°] produces the highest MCF, the Steel / CFRP hybrid square tube with a ply angle of [0° / 90°] produces the highest PCF, and the hybrid square tube with a ply angle of [45° / -45°] has the lowest SEA and PCF. The PCF of the Steel / CFRP hybrid square tube with ply angles of [0° / 90° / 45° / -45°] and [0° / 90°] are 13.82% and 14.97% higher than that of the Steel / CFRP hybrid square tube with a ply angle of [45° / -45°], respectively. lmax An increase of 11.89% and 16.96% respectively.

[0193] In general, the hybrid square tube with 90° fiber layup exhibited higher crashworthiness performance indicators in terms of EA, PCF, and SEA, while the hybrid square tube with 45° fiber layup had a lower S inv and D lmaxThe results show that the steel / CFRP hybrid square tube with a layup angle of [0° / 90° / 45° / -45°] shows relatively good crash resistance under offset loading. Therefore, in subsequent studies, the steel / CFRP hybrid square tube with a layup angle of [0° / 90° / 45° / -45°] is based on the steel / CFRP hybrid square tube with a layup angle of [0° / 90° / 45° / -45°]. n The laying angle is carried out.

[0194] Table 7 Crashworthiness index of Steel / CFRP hybrid square tube with different ply angles

[0195]

[0196] Step 52: Effect of Different CFRP Wrap Lengths

[0197] In order to explore the effect of CFRP wrapping length on the bending characteristics of Steel / CFRP hybrid square tubes under end constraint boundaries, a parametric analysis is performed on Steel / CFRP hybrid square tubes with different CFRP wrapping lengths. The schematic diagram of the arrangement of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths is shown in Figure 2. Fig.23 As shown. Fig.23 The layout diagram of the CFRP package is defined as L w =80, 180, 280, 380mm, other parameters remain unchanged.

[0198] The final deformation mode of Steel / CFRP hybrid square tube with different CFRP wrapping lengths is shown in Figure 2. Fig.24 As shown. Fig.24 It can be seen that three plastic hinges are generated in the Steel / CFRP hybrid square tubes with four CFRP wrapping lengths. Fig.24 As can be seen from (a), the Steel / CFRP hybrid square tube with a CFRP wrapping length of 80 mm has severe local buckling at the left and right end constraints. Fig.24 (b) and Fig.24 (c) shows that the end restraint of the Steel / CFRP hybrid square tube without CFRP wrapping also shows obvious local buckling. This phenomenon is not obvious for the Steel / CFRP hybrid square tube reinforced with CFRP. This is because the offset loading is prone to generate shear force at the end restraint, and the tube wall without CFRP wrapping is relatively thin and the shear resistance is relatively weak. Therefore, the end without CFRP wrapping will show severe local buckling, which will lead to a decrease in the bearing capacity of the Steel / CFRP hybrid square tube.

[0199] Load-displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are shown in Figure 2. Fig.25 As shown. Fig.25 It can be seen that as the length of the CFRP wrapping increases, the load-bearing capacity of the hybrid square tube also increases accordingly. The final intrusion displacement curves of the Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are shown in Figure 2. Fig.26 As shown. Fig.26 It can be seen that when the CFRP wrapping length is 380 mm, the maximum intrusion D of the lower surface profile of the Steel / CFRP hybrid square tube is lmax Minimum. When the CFRP wrapping length is 80mm, the maximum intrusion D of the mixed square tube lmax Maximum intrusion D for CFRP package lengths of 180 mm and 280 mm lmax The difference is not that big.

[0200] In addition, the crashworthiness indices extracted from the load-displacement and final intrusion displacement curves of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths are summarized in Table 8. In order to observe the regular changes more intuitively, Fig. 27 The histogram of Figure 1 compares the crashworthiness of Steel / CFRP hybrid square tubes with different CFRP wrapping lengths. Fig. 27 As can be seen from (a), the Steel / CFRP hybrid square tube with a CFRP wrapping length of 380 mm produced the highest EA and the smallest S inv The Steel / CFRP hybrid square tube with a CFRP wrapping length of 380 mm has the lowest EA and the largest S inv The EA of Steel / CFRP hybrid square tubes with CFRP wrapping lengths of 80 mm and 380 mm are 190.36 kJ and 223.49 kJ, respectively. The corresponding S inv 25.01cm respectively 2 and 20.92cm 2 The EA of the Steel / CFRP hybrid square tubes with CFRP wrapped lengths of 280 mm and 380 mm was increased by 11.69% and 17.40% respectively compared with that of the Steel / CFRP hybrid square tube with CFRP wrapped length of 80 mm. inv and 16.35% respectively. inv The reason for the decrease is that the increase in CFRP wrapping length leads to an increase in CFRP content, which significantly increases the rebound capacity of the hybrid square tube. In addition, after the ends of the hybrid square tube are wrapped with CFRP, the axial force and shear resistance are enhanced, which significantly increases the energy absorption and rebound capacity.

[0201] from Fig. 27 (b) and Fig. 27 As can be seen from (c), the PCF and SEA of the Steel / CFRP hybrid square tube increase with the increase of the CFRP wrapping length, while D lmax The PCF of the Steel / CFRP hybrid square tubes with CFRP wrapping lengths of 280 mm and 380 mm increased by 16.60% and 23.96% respectively, and the SEA increased by 3.5% and 4.9% respectively, and the D lmax They fell by 8.48% and 14.55% respectively.

[0202] In summary, for the bending loading condition under the end constraint boundary condition, especially the offset bending loading condition, the thickness of the clamping part and the loading area of ​​the hybrid square tube end needs to be appropriately strengthened to increase the axial force and its ability to resist shear failure.

[0203] Table 8 Crashworthiness index of Steel / CFRP hybrid square tube with different CFRP wrapping lengths

[0204]

[0205] Step 53: Effect of Different Indenter Shapes

[0206] In actual foreign body intrusion situations, the shape and size of the foreign body are usually uncertain. In order to study the effects of different pressure head shapes on the bending properties of Steel / CFRP hybrid square tubes under quasi-static loading, this section designs four different shapes of pressure heads, which are divided into circular pressure heads, conical pressure heads, trapezoidal pressure heads and square pressure heads according to the cross-sectional shapes. The schematic diagram of the cross-sectional shape and detailed dimensions of the pressure head is shown in Fig.28 As shown. Fig.28 It can be seen that the maximum cross-sectional dimensions of the four pressure heads are all 25 mm, and the shape of the pressure head at one end facing the Steel / CFRP hybrid square tube gradually transitions from sharp to smooth.

[0207] After the indenter is completely unloaded, the final deformation mode of the Steel / CFRP hybrid square tube under the offset loading of different indenters is as follows: Fig.29 As shown in the figure, the pressure head at one end of the Steel / CFRP hybrid square tube gradually changes from sharp to smooth. Fig.29It can be seen that after the conical indenter is unloaded, the plastic deformation area formed on the Steel / CFRP hybrid square tube is small; after the square indenter is unloaded, the plastic deformation area formed on the Steel / CFRP hybrid square tube is large; the plastic deformation area formed after the conical indenter and trapezoidal indenter are unloaded is between the two. Under the offset loading of the conical and circular indenters, the local indentation of the specimen is funnel-shaped and the overall deformation is small. When the specimen is offset loaded by the trapezoidal and square indenters, it is observed that the local indentation width is large and the overall deformation is relatively large. The indentations produced by indenters of different shapes all show an asymmetric plastic deformation mode, which is due to the uneven distribution of axial force on the left and right sides of the Steel / CFRP hybrid square tube caused by the offset loading.

[0208] Load-displacement curves of Steel / CFRP hybrid square tubes under offset loading of different shapes of indenters, such as Fig.30 As shown. Fig.30 It can be seen that the load response curves generated by different shapes of indenters show similar trends. The load of the specimen under offset loading of the conical indenter is smaller than that of the other three shapes of indenters, and as the shape of the indenter changes from sharp to flat, the corresponding bearing capacity and peak force gradually increase.

[0209] In order to quantitatively analyze the intrusion area of ​​the Steel / CFRP hybrid square tube under different shapes of indenter offset loading, the final intrusion displacement of each measuring point is plotted on Fig.31 In. From Fig.31 It can be seen that the maximum intrusion amount after the square indenter is unloaded is the largest, while the maximum intrusion amount after the conical indenter is unloaded is relatively small. This is because the contact area between the square indenter and the specimen is much larger than that of the conical indenter, and the plastic deformation energy generated is also relatively larger, resulting in the need to improve the ability of the Steel / CFRP hybrid square tube to resist bending deformation accordingly, so the maximum intrusion amount is also larger.

[0210] In addition, the crashworthiness indices extracted from the load-displacement and final intrusion displacement curves under different shapes of indenter offset loading are summarized in Table 9. In order to observe the regular changes more intuitively, Fig.32 The histogram of compares the crashworthiness of Steel / CFRP hybrid square tubes under different shapes of indenters with offset loading. Fig.32 By comparing the crash resistance performance of EA, PCF, SEA, D lmax , MCF and S invBoth gradually increase as the shape of the indenter becomes flatter. The EAs of the Steel / CFRP hybrid square tubes obtained under offset loading of conical, circular, trapezoidal and square indenters are 176.47J, 223.49J, 247.19J and 265.47J, respectively. Compared with the loading of the conical indenter, the EA and SEA obtained by the indenters of other shapes increased by 26.64%, 40.07% and 50.43%, respectively. The SEAs of the Steel / CFRP hybrid square tubes obtained under offset loading of circular, trapezoidal and square indenters are 176.47J, 223.49J, 247.19J and 265.47J, respectively. Compared with the loading of the conical indenter, the EA and SEAs obtained by the indenters of other shapes increased by 26.64%, 40.07% and 50.43%, respectively. inv Compared with the conical indenter loading, the PCF increased by 10.11%, 32.00% and 46.74%, respectively, and the D lmax The square indenter-loaded Steel / CFRP hybrid square tube showed higher energy absorption and greater peak force, which is because the contact area between the square indenter and the specimen is large, which leads to more energy dissipation. The overall deformation of the Steel / CFRP hybrid square tube with square indenter-loaded offset is larger, which leads to an increase in the maximum intrusion amount and intrusion area of ​​the specimen. Therefore, from the perspective of collision safety, when designing anti-bending structures, the boundary value of larger intrusion foreign matter should be considered, that is, a relatively large safety factor should be adopted.

[0211] Table 9 Crashworthiness index of Steel / CFRP hybrid square tube under different shapes of indenter offset loading

[0212]

[0213] This paper takes Steel / CFRP hybrid square tube as the research object, and reveals the bending performance of Steel / CFRP hybrid square tube under different loading positions based on experimental methods. The finite element model and theoretical prediction model of Steel / CFRP hybrid square tube under offset loading are constructed and verified, and the influence of offset distance on the bending energy absorption mechanism is revealed based on the theoretical prediction model. The influence of simultaneous changes in multiple parameter domains under offset loading on the bending characteristics is discussed. In addition, the influence of ply angle, CFRP wrapping length and pressure head shape on the bending characteristics is also explored.

[0214] (1) The crash resistance performance of the Steel / CFRP hybrid square tube under mid-span loading is lower than that under 1 / 3 span loading and 1 / 4 span loading. The EA of the Steel / CFRP hybrid square tube under 1 / 3 span loading and 1 / 4 span loading is 14.62% and 27.46% higher than that under mid-span loading, respectively. invThe closer the loading position is to the constraint end, the larger the EA is, and the larger the corresponding SEA is. lmax and the corresponding S inv This is because the closer the loading position is to the constraint end, the higher the degree of participation of the axial force, which in turn increases the bearing capacity, increases the energy absorption, and reduces the intrusion area.

[0215] (2) A theoretical model of energy absorption of Steel / CFRP hybrid square tubes under offset loading was established and compared with the experimental results of 1 / 3 span and 1 / 4 span loading conditions. The maximum errors were 0.08% and 6.49%, respectively, indicating that the theoretical model of Steel / CFRP hybrid square tubes under offset loading can effectively predict the experimental results. The influence of different offset distances was studied. When the offset distance is less than 80 mm, EA will increase with the increase of offset distance. However, if the offset distance is too large, the participation of shear force will significantly reduce the EA of Steel / CFRP hybrid square tubes. From the multi-parameter coupling effect analysis, it can be found that Steel thickness has a significant effect on EA, PCF, MCF, S inv , D lmax The offset distance ΔD has the greatest impact on SEA.

[0216] (3) The hybrid square tube with 90° fiber layup exhibits higher crashworthiness performance in terms of EA, PCF, and SEA, while the hybrid square tube with 45° fiber layup has a lower S inv and D lmax The steel / CFRP hybrid square tube exhibits higher crashworthiness performance indicators in terms of performance. This is mainly due to the different failure characteristics of the CFRP tube in the inner layer of the Steel / CFRP hybrid square tube caused by different fiber layup angles, which changes the relative resistance to bending and indentation. The Steel / CFRP hybrid square tube fully wrapped with CFRP exhibits better bending performance. For bending loading conditions under end constraint boundary conditions, especially offset bending loading conditions, the thickness of the clamping part and loading area at the end of the hybrid square tube needs to be appropriately strengthened to increase the energy absorption and shear failure resistance of the structure. The Steel / CFRP hybrid square tube subjected to offset loading by a square pressure head exhibits relatively large energy absorption and overall deformation. As the shape of the pressure head facing one end of the Steel / CFRP hybrid square tube gradually transitions from sharp to gentle, the crashworthiness indicators all show an upward trend.

Claims

1. The bending performance prediction method of Steel / CFRP hybrid square tube based on different loading positions is characterized by The following steps are involved: Step 1: Conduct an experimental study on the Steel / CFRP hybrid square tube under offset loading by arranging an offset loading experiment to form a final deformation comparison and analyze the mechanical properties of the Steel / CFRP hybrid square tube under different loading positions; Step 2: Construct a finite element model of the Steel / CFRP hybrid square tube under offset loading; Step 3: Construct a theoretical prediction model for Steel / CFRP hybrid square tubes under offset loading to obtain the effect of offset distance on the theoretically predicted energy absorption; Step 4: Analyze the multi-parameter coupling effect under bias loading; Step 5: Analyze the factors affecting the bending characteristics; including the influence of different ply angles, the influence of different CFRP wrapping lengths, and the influence of different indenter shapes.

2. The method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions according to claim 1 is characterized in that In the step 1: the quasi-static bending test of the Steel / CFRP hybrid square tube under offset loading is carried out on an MTS-322 hydraulic servo control testing machine, and both ends of the specimen are locked and fixed by the upper and lower clamping devices of the U-support frame, and also include a rectangular clamp block. By adjusting the relative position relationship between the rectangular clamp block and the U-shaped clamp, the bending characteristics of the Steel / CFRP hybrid square tube under different loading positions are studied, and different loading position test scenarios are set by adjusting different effective spans.

3. The method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions according to claim 1 is characterized in that In the step 2: the geometric dimensions of the finite element model of the Steel / CFRP hybrid square tube are the same as those of the specimen in the experiment, the degrees of freedom on both sides are constrained, the loading speed of the pressure head is set to 1000 mm / s, the downward compression displacement is set to 22 mm, and the grid sizes of the specimen and the pressure head are set to 2 mm and 5 mm, respectively; the offset distance ΔD of the pressure head loading is set, which is defined as the offset distance between the loading point and the center line of the Steel / CFRP hybrid square tube; the effective span of the Steel / CFRP hybrid square tube is 300 mm, and the offset distances ΔD of the 1 / 3 span loading condition and the 1 / 4 span loading condition are set to 50 mm and 75 mm, respectively.

4. The method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions according to claim 1 is characterized in that The step 3 includes an analytical solution for the large deflection of the Steel / CFRP hybrid square tube under offset loading; under the offset loading condition, for the Steel / CFRP hybrid square tube with end clamping constraints, the local deformation effect at the loading position is ignored; it is assumed that the other parts of the slender Steel / CFRP hybrid square tube are rigid and deform globally in an integral manner; three hybrid plastic hinges are developed at the loading position and the end support of the Steel / CFRP hybrid square tube respectively; the span of the hybrid square tube is L, the loading point is located at a distance of L1 from the left support end, and the offset distance between the loading point and the center line of the span of the hybrid square tube is ΔD; under the external concentrated load P b The maximum deflection W of the mixed square tube occurs under the action of b ; The equilibrium equation of the moment is obtained, as shown in formula (1): Where M bm is the bending moment at the loading point, F b is the lateral load, M b is the bending moment at the end support, and M b =M bm ; Transform formula (1) to obtain the concentrated load P b The lateral displacement W of the loading point b The relationship expression between is shown in formula (2). Assume that the total extension of the left free body with length L1 is a L , its calculation expression is shown in formula (3) a L =a L1 +a L2 (3) where a L1 and a L2 are the axial extensions of the left free body end; Combining equation (3) and equation (4) can further simplify equation (5) According to the geometric relationship, the left rotation angle ψ L The calculation expression of is shown in formula (6): Similarly, assume that the total extension of the right free body with length L2 is b R , its calculation expression is shown in formula (7) b R =b R1 +b R2 (7) where b R1 and b R2 are the axial extensions of the left free body end respectively; according to the geometric relationship, formula (8) Combining equation (7) and equation (8) to further simplify equation (9) According to the geometric relationship, the right rotation angle ψ R The calculation expression of is shown in formula (10): The ratio of axial elongation to curvature and bending deflection W in the left and right free bodies b The relational expression of is shown in formula (11): On the other hand, the relevant flow rule for the plastic yield criterion is expressed as follows: Combining equations (11), (12) and (13), we can obtain the expression of the bending deflection of the Steel / CFRP hybrid square tube under offset loading: Assume that the length L1 of the left free body is less than half of the span, and the length of the right free body is greater than half of the span. Therefore, according to the geometric relationship, L1 and L2 are expressed by the relationship between the offset distance and the span: L1=L / 2+ΔD (15) L2=L / 2-ΔD (16) Substituting equations (11), (15), and (16) into equation (1), the calculation expression of the analytical solution of the large deflection of the Steel / CFRP hybrid square tube under offset loading is obtained, as shown in equation (17); Among them, t m Indicates Steel thickness, t c Indicates the thickness of CFRP, P b1 , P b2 , P b3 , P b4 is the loading load under different bending deflection Wb, σ m represents the material yield stress of Steel square tube, σ c Indicates the stress of Steel square tube in tension and compression; For each interval stage in formula (17), b -W b The curve is integrated and the energy is accumulated. Therefore, the plastic bending deformation energy E of the Steel / CFRP hybrid square tube under offset loading is obtained. b and deflection W b The relational expression of is shown in formula (18); 5. The method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions according to claim 1 is characterized in that In the step 4: analyzing the correlation between the steel thickness, the CFRP thickness, the section width and the offset distance, and finding the main effect of the correlation between the steel thickness, the CFRP thickness, the section width and the offset distance on the response; The linear effect of the normalized design parameters is calculated using a linear regression model, where the value range of the normalized design parameters is mapped to [0,1]. The calculation expression of the linear effect value between each design parameter x and the output response f(x) is shown in formula (19): f(x)=b0+b1x (19) The slope b1 of the line in the linear regression model represents the influence of the design parameters on the response, and b0 represents the constant term in the linear regression model. If the line is close to horizontal, it means that the design parameters have almost no effect on the output response; If the line tends to be vertical, it means that the design parameters have a greater impact on the output response; A positive slope of the line indicates that the design parameter is positively correlated with the output response, while a negative slope indicates that the design parameter is negatively correlated with the output response.

6. The method for predicting the bending performance of Steel / CFRP hybrid square tubes based on different loading positions according to claim 1 is characterized in that In the step 5: parameter analysis is used to study the influence of the ply angle, CFRP coating length and indenter shape on the bending characteristics of the Steel / CFRP hybrid square tube under the offset loading condition; the default boundary condition of the 1 / 3 span loading condition is used, and the following geometric parameters of the Steel / CFRP hybrid square tube are set to default values: the span is set to 300 mm, the section width is 28 mm, the Steel thickness is 1 mm, the CFRP thickness is 1 mm, the thickness of each CFRP layer is 0.1 mm, the stacking order of the ply angle is [0° / 90° / 45° / -45°], the indenter diameter is 25 mm, and the indenter offset distance is 50 mm; when one influencing factor changes, the other factors remain at the default values.

Images